English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Numerical analysis of conserved field dynamics has been generally performedwith pseudo spectral methods. Finite differences integration, the commonprocedure for non-conserved field dynamics, indeed struggles to implement aconservative noise in the discrete spatial domain. In this work, we present anovel method to generate a conservative noise in the finite differencesframework, which works for any discrete topology and boundary conditions. Weapply it to numerically solve the conserved Kardar-Parisi-Zhang (cKPZ)equation, widely used to describe surface roughening when the number ofparticles is conserved. Our numerical simulations recover the correct scalingexponents $\alpha$, $\beta$, and $z$ in $d=1$ and in $d=2$. To illustrate thepotentiality of the method, we further consider the cKPZ equation on differentkinds of non-standard lattices and on the random Euclidean graph. This is thefirst numerical study of conserved field dynamics on an irregular topology,paving the way to a broad spectrum of possible applications.

From noise on the sites to noise on the links: discretizing the conserved Kardar-Parisi-Zhang equation in real space